Ionization of the3dσmolecular orbital in heavy-ion collisions

As suggested previously, in a heavy-ion collision the sum of the total $L$-vacancy-production cross section of the higher-$Z$ partner and of the $K$-vacancy-production cross section of the lower-$Z$ partner, close to $K-L$ level-matching conditions, represents the vacancy-formation cross section in the $3d\sigma$ molecular orbital. It is found empirically that at a given projectile velocity $v_1$ the $3d\sigma$ cross section depends mainly on the united-atom $Z$, independent of the projectile $Z\left(Z_1\right)$, between $Z_1=28\mathrm{} \mathrm{and} 53$. A united-atom ionization model of Briggs is evaluated in the semiclassical approximation. The results provide an upper-limit estimate for the $3d\sigma$ cross section, which reproduces quantitatively its empirical $v_1$ and $Z$ dependence and its order of magnitude. The results do not imply, though, that other vacancy-production mechanisms may not be as, or more, important than ionization.